This book is a captivating account of a professional mathematician's experiences conducting a math circle for preschoolers in his apartment in Moscow in the 1980s. As anyone who has taught or raised young children knows, mathematical education for little kids is a real mystery. What are they capable of? What should they learn first? How hard should they work? Should they even "work" at all? Should we push them, or just let them be? There are no correct answers to these questions, and the author deals with them in classic math-circle style: he doesn't ask and then answer a question, but shows us a problem--be it mathematical or pedagogical--and describes to us what happened. His book is a narrative about what he did, what he tried, what worked, what failed, but most important, what the kids experienced. This book does not purport to show you how to create precocious high achievers. It is just one person's story about things he tried with a half-dozen young children. Mathematicians, psychologists, educators, parents, and everybody interested in the intellectual development in young children will find this book to be an invaluable, inspiring resource. In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession. Titles in this series are co-published with the Mathematical Sciences Research Institute (MSRI).
This book explores ways of developing continuity in children's learning from 3-7. It describes three case studies in which tutors on ITT courses work with early years practitioners in a variety of schools, each linked to a pre-school setting.
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This, the third volume of the History of the Peninsular War, covers a longer period than either of its predecessors, extending over the sixteen months from Wellington’s arrival at Badajoz on his retreat from Talavera (Sept. 3, 1809) to the deadlock in front of Santarem (Dec. 1810), which marked the end of Masséna’s offensive campaign in Portugal. It thus embraces the central crisis of the whole war, the arrival of the French in front of the Lines of Torres Vedras and their first short retreat, after they had realized the impossibility of forcing that impregnable barrier to their advance. The retreat that began at Sobral on the night of Nov. 14, 1810, was to end at Toulouse on April 11, 1814. The armies of the Emperor were never able to repeat the experiment of 1810, and to assume a general and vigorous offensive against Wellington and Portugal. In 1811 they were on the defensive, despite of certain local and partial attempts to recover their lost initiative. In 1812 they had to abandon half Spain—Andalusia, Estremadura, Asturias, La Mancha, and much more,—despite of Wellington’s temporary check before Burgos. In 1813 they were swept across the Pyrenees and the Bidassoa; in 1814 they were fighting a losing game in their own land. Rightly then may Masséna’s retreat to Santarem be called the beginning of the end—though it was not for a full year more that Wellington’s final offensive commenced, with the investment of Ciudad Rodrigo on Jan. 8, 1812. The campaign of Bussaco and Torres Vedras, therefore, marked the turning-point of the whole war, and I have endeavoured to set forth its meaning in full detail, devoting special care to the explanation of Wellington’s triple device for arresting the French advance—his combination of the system of devastation, of the raising of the levée en masse in Portugal, and of the construction of great defensive lines in front of Lisbon. Each of these three measures would have been incomplete without the other two. For the Lines of Torres Vedras might not have saved Portugal and Europe from the domination of Napoleon, if the invading army had not been surrounded on all sides by the light screen of irregular troops, which cut its communications, and prevented it from foraging far afield. Nor would Masséna have been turned back, if the land through which he had advanced had been left unravaged, and if every large village had contained enough food to subsist a brigade for a day or a battalion for a week. The preparations, the advance, and the retreat of Masséna cover about half of this volume. The rest of it is occupied with the operations of the French in Northern, Eastern, and Southern Spain—operations which seemed decisive at the moment, but which turned out to be mere side-issues in the great contest. For Soult’s conquest of Andalusia, and Suchet’s victories in Aragon, Catalonia, and Valencia only distracted the imperial generals from their central task—the expulsion of Wellington and his army from the Peninsula. Most readers will, I think, find a good deal of new information in the accounts of the siege of Gerona and the battle of Ocaña. The credit due to Alvarez for the defence of the Catalonian city has never been properly set forth before in any English history, nor have the details of Areizaga’s miserable campaign in La Mancha been fully studied. In particular, the composition and strength of his army have never before been elucidated, and Appendices V, VI of this volume consist of absolutely unpublished documents. To be continue in this ebook...
